Several points should be made.
As the state did not record births until 1850 (and the Church did) etc, I was
informed by an expert at the Family History Library in Salt Lake City that
these data were collected by the local church for the state for convenience.
These included Jewish records >from about 1800 to 1854.
Arthur Kurzweil, in >from Generation to Generation, discusses his discovery
where his ancestor (a descendant of the Stropkover Rebbe) took the surname of
his mother. This is in the first chapter.